Fekete's Lemma: Proof & Understanding

[CoachZ]

Fekete's Lemma states that if {a_n} is a real sequence and a_(m + n) <= a_m + a_n, then one of the following two situations occurs:
a.) {(a_n) / n} converges to its infimum as n approaches infinity
b.) {(a_n) / n} diverges to - infinity.

I'm trying to figure out a way to show either of these things happen but can't seem to do it. Does anyone have the proof of this or have suggestions to go about proving it.

 

[foxjwill]

a) Suppose the {a_n/n} converges to some number A. Show that A is the inf.